-x-(6xy%5E-3).jpeg "(3x^-2y) X (6xy^-3)")
Simplifying Algebraic Expressions: (3x^-2y) x (6xy^-3)
This article will guide you through simplifying the algebraic expression (3x^-2y) x (6xy^-3).
Understanding the Rules
Before we start simplifying, let's review the key rules we'll be using:
- Product of powers: When multiplying exponents with the same base, you add the powers. x^m * x^n = x^(m+n)
- Negative exponents: A negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. x^-n = 1/x^n
Step-by-Step Simplification
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Rearrange the terms: To make the simplification clearer, let's rearrange the expression: (3 * 6) * (x^-2 * x) * (y * y^-3)
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Multiply the coefficients: 18 * (x^-2 * x) * (y * y^-3)
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Apply the product of powers rule: 18 * x^(-2+1) * y^(1-3)
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Simplify the exponents: 18 * x^-1 * y^-2
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Apply the negative exponent rule: 18 * (1/x) * (1/y^2)
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Combine the terms: 18 / (xy^2)
Final Result
The simplified form of the expression (3x^-2y) x (6xy^-3) is 18 / (xy^2).